A flexible hierarchical quantile spatial autoregressive model

Abstract

This work introduces a new class of nested models which extends the literature standard combination of spatial autoregressive model for areal data with parametric quantile regression. Besides, the new proposed model can incorporate a hierarchical structure, allowing it to deal with clustered data. Such approach produces a robust and flexible statistical method for modeling the quantiles of areal data distributed in a hierarchically geographical setting. The proposed model is evaluated using a well-known house pricing data and a simulated study. The hierarchical version is also applied to a real data concerning a math score related to public high schools within the Metropolitan area of Rio de Janeiro, Brazil.